ESO Concert June 7^th 2025

As promised here are my programme notes for the ESO concert on June 7th at Grey Friars Kirk at 7:30 pm. The conductor is a guest conductor Kentara Machida Led by Shenna Jardine who has a solo part in Orkney Wedding. The soloist for the Prokofiev Violin Concerto is Viktor Seifart. The notes are quite brief due to printing costs. I would normally write extended versions of the notes but given the brevity of the pieces it hardly seems worth it this time. Anyway may be see some of you at the concert. Also if anyone plays in an amateur orchestra and you are looking for someone to write the programme notes please contact me at my local e-mail address. 

chrisf19572002@yahoo.co.uk

Cuban Overture George Gershwin (1898-1937)

In 1932 Gershwin visited Havana for a short break. The irregular rhythms and exotic percussion instruments, such as the maracas, bongos and gourd associated with Cuban music, inspired Gershwin to write this overture. It is a tri-partite work A-B-A consisting of a lively opening section which makes use of the exotic percussion instruments and Cuban rhythms. The second section introduced by the oboe is a typical Gershwin blues melody, which evokes sultry Latin American nights. The first section is repeated with variations, ending the overture on a lively note. The overture was premiered in August 1932 at an all-Gershwin concert in New York and became an instant success.

 Violin Concerto No 2 in G minor Sergei Prokofiev (1891 – 1953)

I Allegro moderato, II Andante Assai, III Allegro ben marcato.

In 1935 Prokofiev was preparing to resettle in Russia, but he realised that in order to appease Stalin, he would have to abandon his earlier Avant Garde style. This led to a change which he termed back to simplicity. Alongside other pieces such as Peter and the Wolf and the Lieutenant Kije suite, he composed his second violin concerto.

The first movement begins with a lamenting statement in G minor by the solo violin based on a five beat pattern. The listener is thrown off balance by the entrance of the orchestra in a different tonality and the movement continues filled with edgy biting sarcasm. A more lyrical second theme is introduced hinting at the possibility of reaching some sort of tonal stability but the restless mood continues. The movement ends shrouded in mystery, with muted horns and pizzicato strings. In contrast to the first movement, the second movement is a lyrical one where the violin is accompanied by pizzicato strings. It is a virtual ballet scene without dancers. At the end the soloist plays pizzicato whilst the orchestra plays the main melody. The sunny innocence evaporating into darkness. The final movement is a wild exhilarating dance filled with biting sarcasm and demonic shrieks, reminiscent of Mahler. As the movement progresses it becomes rhythmically unstable. Towards the end, the violins’ furious music is accompanied by the thud of the bass drum.

 Prokofiev composed the piece for his friend the French violinist Robert Soetens. It was premiered on 1 December 1935 in Madrid by the Madrid Symphony Orchestra. It was the last major piece that Prokofiev composed before he returned to Russia.

Four Scottish Dances Malcolm Arnold (1921 – 2006)

1 Pesante II Vivace III Allegretto IV Con Brio

This piece was composed in 1957 for the BBC Light Music Festival. It was inspired by but not based on Scottish country folk tunes and dances. The first dance is in the style of a Strathspey, a dance in 4/4 time, featuring dotted rhythms and Scotch snaps. The second is a lively reel. The third dance evokes a calm summers day in the Hebrides, and the suite ends with a lively fling. The dances as a whole invoke Scotland (or at least Arnold’s idea of what Scottish music should sound like). It  makes use of Arnold’s skill in devising complex rhythms.

 

“An Orkney Wedding with Sunrise” Peter Maxwell Davies (1934-2016).

Peter Maxwell Davies established a reputation as an Avant-Garde composer in the 1960’s. However in 1970 he settled in the Orkneys, where he decided to help the locals with their music making and published a number of works, which complement his more complex works. Maxwell Davies attended a wedding in 1978 and this inspired the current piece, which has the dramatic entrance of a bagpipe player in full Scottish regalia at the end. He describes the work as follows

 “It is a picture postcard. We hear the guests arriving, out of extremely bad weather. This is followed by a processional and a first glass of whisky. The band tunes up and we get on with the dancing, which becomes ever wilder, until the lead fiddle can hardly hold the band together. We leave the hall into the cold night. As we walk home across the island, the sun rises to a glorious dawn. The sun is represented by the highland bagpipes, in full traditional splendor.”

The work was commissioned by the Boston Pops Orchestra and was premiered on May 10 1985. It has become one of his most popular pieces and is performed on a regular basis.

 

 

Danzon No 2 Arturo Marquez (b 1950)

Arturo Marquez is one of Mexico’s finest living composers. As with many of the other composers in this concert, he established his reputation as an Avant-Garde composer. However after composing his first Danzon in 1990, he was drawn to the original style and fell in love with Latin ballroom dancing music. The Danzon is the official dance of Cuba, that evolved from the habanera. It is a slow formal dance, requiring set foot work around syncopated beats. The dance incorporates elegant pauses whilst the couples listen to virtuoso instrumental passages, played by a charange or tipica ensemble.

The dance begins with a slow introduction by the clarinet accompanied by the claves that Gershwin called ‘Cuban Sticks’. A duet between the oboe and clarinet ensues. The orchestra changes the mood and becomes more forceful. A piccolo solo leads into a lyrical section led by solo violin. This draws to a close and the dance becomes more boisterous than before. With the music on the brink of pandemonium, the orchestra unites in repeating a single note continuously, ending with an exciting conclusion.

Needless to say the piece has become one of Arturo Marquez’s most popular and it has been dubbed the second Mexican National Anthem.

Chris Finlay May 2025.

Hello sorry its been a long time

 Hi everyone who is interested in this blog and its contents. First I must apologise that I have not made any posts since 2022 which is about 3 years ago. I have been engaged in a number of activities. One of the most interesting is the fact that I was asked by a Friend of mine if I would consider writing the programme notes for their orchestra which some of my colleagues at work play in. It is the Edinburgh Symphony Orchestra

Edinburgh Symphony Orchestra – Established 1963 Conducted by Gerard Doherty. 

 and I have been producing notes for them for about 4 years now, The next concert is on June 7th at Greyfriars Kirk. It is somewhat lighter than usual consisting mainly of Dance music. Two allegedly Scottish pieces by Malcom Arnold and Maxwell Davies. It is probably fair to say that the music reflects their idea of what Scottish Music should sound like rather than anything genuinely Scottish. Also two pieces in a Cuban Style one by Gershwin namely his Cuban Overture and another by Marquez a contemporary Mexican composer his Danzon No 2, The Danzon is a formal Cuban dance and Marquez has composed a number of these. Finally the centre piece of the concert is Prokofiev's 2nd Violin Concerto a piece he composed before preparing to settle back in Russia and in order to appease Stalin he moved away from his earlier Avant-Garde style. It is a theme common to this concert that composers who were considered Avant Garde wrote more popular style of music. Unfortunately these pieces seem to have eclipsed their more serious work so whilst almost every Scot will have heard Maxwell Davies's Orkney Wedding with Sunrise, they wont be familiar with his complex Symphonies or String Quartets. Anyway I shall post the program notes for this concert quite soon and also the previous notes. 

As far as physics goes I have more or less completed my notes on Deep Inelastic Neutrino Nucleon Scattering part of the problem is struggling with Word and its really awkward way of numbering equations, So that instead of physics I end up farting around trying to make sure that the equation numbering is consistent with each other. Anyway on the last lap now and hope to finish by end of July. 

Finally for now as times winged chariot is pressing on I have decided to concentrate on important things. One of these is trying to read the essential classics of literature. In the 1950's the Encyclopedia Britannica published a series entitled 'Great Books of the Western World' 

Great Books of the Western World - Wikipedia it is possible to access these via the Internet Archive library

Encyclopædia Britannica - Great Books Of The Western World - Volumes 1-54 : Encyclopaedia Britannica : Free Download, Borrow, and Streaming : Internet Archive

There is also a shortened reading list available 

The 10 Year Reading Plan for the Great Books of the Western World - ThinkingWest

I intend to use this as a guide but not necessarily in the same order. I am currently interested in reading the classics of political philosophy and I have started with Machiavelli and I shall share my thoughts on him on this blog. 

Anyway sorry to those who have missed me I will try and post more regularly in future 

Notes on Blackbody radiation

 Hi folks sorry  I have been silent for a while anyway I have beeen busy for about a year writing up some notes on Blackbody radiation. This is a fairly straightforward run through of the basic ideas of Statistical Mechanics and how Planck managed to finally obtain the correct formula by making the guess that electromagneitic energy is quantised. For Planck this was just a ruse and he thought little about it. However it took Einstein to take the idea seriously and he applied it to calculate the specific heat of solids and almost got the correct low temperature behaviour. It was left to Debye to improve on Einstein's model by performing a numerical integration over all frquencies. So Debye is a better physicist than Einstein 😅😅Well at least in that respect. 

I must admit I have had a love hate relationship with Statistical Physics over the years we had a pretty bad lecturer a certain Dr Jones at Exeter university who was (is) a really clever guy but his lectures bore no real resemblance to conventional statistical physics texts and so I and a friend who I was studying with at the time were left scratching our heads and wondering what the subject was all about. With these set of notes I have finally laid the ghost of that experience to reat and now feel I have enough background in statistical physics to understand its applications in Astro-physics especially the physics of the early universe and the calculation of the Helium abundance in the universe by Peebles and other people. 

Of course everyone knows that the Cosmic Background radiaton is a black body and I produce a graph comparing Planck's formula with the FIRAS data obtained from the COBE satellite. I also show how to do the Numerical Integration to get Debye's prediction of the specific heat of silver at low temperatures. 

There are some pretty interesting integrals which invove the Product of the Riemann Zeta function and the Gamma Function. and I show how these are derived unlike most books which just state the formula. As this formula is ubiquitous in Astro-Physical applications then I have enclosed it in a red box at the end of a fairly long appendix at the end. 

Anyway I hope you find the notes useful I now have all the building blocks in place to understand the Peebles calculation and over the next year or two I hope to finally finish this culminating in a code which traces the abundance of the Light elements during the first three minutes after the biig bang 

Here is a link to the file 

https://drive.google.com/file/d/11tpWAP4vh1ywl9ITv8opKCCsiJBws2oP/view?usp=sharing

Cambridge NST Maths year 1 2019 Paper 2 solutions

 Here is the second in a sequence of my solutions to the Cambridge NST maths papers, This one is for the second of the papers set for the first year students in 2019 the last year before COVID. You can access it here 

https://drive.google.com/file/d/1SSePjGdcGjWatVFNHh5kVzYORGgaBUrD/view?usp=sharing

I have previously published my solutions to the first of the papers and for convenience I post the link again here for those who missed it first time around

https://drive.google.com/file/d/1SSePjGdcGjWatVFNHh5kVzYORGgaBUrD/view?usp=sharing

So there you have it a complete set of answers to the first year papers for NST students at Cambridge for 2019. Most of them will have sat there finals last summer and I hope they did well. 

I apologise in advance for any typos spelling errors etc. A review of the paper follows 

Again just like the first paper this was quite challenging and unfortunately I was unable to answer a question on Parseval's theorem properly. On the whole though I think I got the questions out, but I doubt if I could do well under exam conditions. 

Anyway just like the first paper there were 10 short questions which were relatively straightforward once you decoded what the examiner was getting at. The questions included solving a first order differential equation by the integrating factor method. Deriving a recurrence relation for an Integral (something they love testing people on). Calculating the stationary values of a function f(x,y). A slightly confusing question on pronability I really need more practice at questions involviing conditional probability. A volume integral and a surface integral. All this should take no longer than 30 mins but I suspect I would take a lot longer. Again there is no time to think and in the rush you would probably end up making silly mistakes,

The core of the paper is 10 questions of which answers to five must be submitted. The last two questions are reserved for those students deemed clever enough to do some advanced topics although I didn't think they were particularly difficult. 

Anyway here are the questons 

Question 11 was a geometric one involving the equation of a plane and finding the volume of the parallipped enclosed by 3 vectors. This was relatively straightforward once I had reminded myself of the vector equation of a plane. But there were quite a few parts. Although the question asked for a few diagrams I had the luxury of using MATLAB to draw the relevant pictures/ Not very exciting I must admit

Question 12 . Involved fiinding the stationary points of a function in f(x,y) and drawing a contour plot showing the function and the gradient. This was tedious but relatively straightforward and again I was able to use MATLAB to draw some pretty pictures. 

Question 13 Involved calculating the line integral of a vector function F for various paths and also finding a function satisfying curl F = 0. (a conservative function). I hadn't done a question like this for ages so I had to remind myself of how you go about calculating such things but it was relatively straightforward although finding the conservative function involved a little guesswork so not very satisfactory.

Question 14  Involved some questions on probability density functions. and evaluating their products and change of  variables. It was ok but not a very exciting topic. 

Question 15  This was a set of questions on solving second order differential equations with constant coefficients my favourite topic at this level. The first question was a homogeneous equation with boundary conditions and relatively straightforward to solve. The second part was an inhomogenous equation and whilst finding the complementary function was relatively straightforward. In order to find the particular integral you had use a function of the form  x^n f(x) and increase n until you found one that worked. This took a couple of goes and so would have been quite time consuming under exam conditions how nice of them 😊. The last part involved solving two differential equations simultaneously some what surprisingly they don't seem to teach how to solve such systems using matrices and their eigenvectors unlike the open university courses MST210 or MST224 so this is one occasion wihere the open university is better than Cambridge. Anyway compared to the tedium of the last few questions this was a delight to do. 

Question 16   This question was all about calculating various surface integrals and the flux of a field through a surface. It got a bit fiddly but again was relatively straight forward. Another boring topic though I much prefer solving differential equations 

Question 17 This was a boring question on matrices again pretty straighrforward but you have to know the definitions and again there were so many parts to the question. Give me calculus questions any day

Question 18  This was a question on Fourier series you had to find the Fourier series for cosh(x) then differentiate to get the Fourier series for sinh(x). For this topic you really need to be on top of integration by parts. The last part of the question then asked you to use Parsevals theorem to show that the integral of (cosh(x)-sinh(x))^2 over the interval was sinh(2) . I tried this a couple of times but I couldn't get the expansions to cancel out to leave sinh(2) so unfortunately I was unable to complete the paper properly. However if you integrate the function directly it comes out relatively straightforwardly. 

So the two questions for the so called advanced students were as follows 

Question 19 was on Lagrangian multipliers and you had to find the optimum volume of a cylinder the optimum volume of a cone inscrbed in a sphere and then prove that the Arithmetic mean is >= to the geometric mean. I confess to nor really understanding this topic although I can go through the motions and I find it difficult to tell whether I am finding a minimum or a maximum. For the cone inscribed inside a sphere I found it easier to just finding the maximum volume directly. I'll let you solve this question using Lagrangian Multipliers fot your self. 

Question 20  A relatively straightforward question on solving partial differential equations using separation of variables. Two first order ones and a question on the diffusion equaton. This is really a warm up for what comes next year so you aren't asked to solve the differential equations in spherical or cylindrical coordinate systems or use Lagrange Polynomials or Bessel functions or any of the other exotic functions out there. So a bit boring really 

Overall conclusion is that this was an exercise worth doing to remind myself and extend my mathematical knowledge a bit. I think on the whole I preferred the first paper as it seemed to cover slightly more interesting topics. Apart from the two quesitions on differential equations this paper could be described as worthy but dull. 

The second year papers for this year beckon next and I hope that I find them a bit more interesting than this one. Hopefully I can finish them by June next year

I would urge you to have a go for yourself and I hope you find these solutions useful 

Thermodynamics

 The laws of thermodynamics are fundamental for understanding the  structure of matter and the transfer of heat. Remarkably they stand by themselves and have no need of any microscopic underpinning This point is often missed in treatments of thermodynamics which quickly move onto statistical physics and don't encourage physicists to develop their powers of thermodynamic reasoning. 

The best account of thermodynamics I know of is given in Longairs book 

https://www.amazon.co.uk/Theoretical-Concepts-Physics-Second-Alternative/dp/052152878X

Which then goes onto discuss how the attempts to model black body radiation broke down using classical physics thus paving the way for Planck and Einstein to introduce quantum mechanical ideas. It really is a fascinating story and shows that there is more to quantum mechanics than the development of Schrodinger's equation 

In general terms a good overall book on Thermodynamics is the classic by Zemansky 

https://www.amazon.co.uk/Heat-and-Thermodynamics-Fifth-edition/dp/B00X4VPZ0C/ref=sr_1_12?crid=32NLWLWHKDY3O&dchild=1&keywords=heat+and+thermodynamics+zemansky&qid=1633373359&s=books&sprefix=Zemansky+%2Cstripbooks%2C173&sr=1-12

Anyway thermodynamics has many applications Chandresekhar used it to work out the General equations of stellar structure without any need to know the internal structure of a star 

Here is my tribute to Thermodynamics and I would encourage people to study it in it's own right 

                                 Thermodynamics

 

Three laws oh so neat,

Describing the nature of heat.

The first says you cannot win,

You wont get back more than you put in.

 

But if it’s heat, there’s a permanent loss,

That is only regained at greater cost.

Finally there will come a great big chill,

Where all that there is, will stand still.

Lasers

 I was challenged by a work colleague to see if I could write a poem about lasers. The result is given below. Just like supeconductivity lasers are another successful application of quantum mechanics which again no agonising about it's meaning will ever produce a laser Ironically given that Einstein rejected the later formulation of quantum mechanics it was Einstein who worked out the basic theory of spontaneous emission on which the laser is based in 1918  This is a purely statistical argument, which again might surprise people as Einstein is allegedly supposed to have claimed that God does not play dice. Well in the early days of quantum mechanics it was Einstein who used statistical arguments to work out the consequences of the photo-electric effect and applied statistical reasoning to work out the Heat capacity of solids. So the idea that Einstein didn't like statistical reasoning is just incorrect. Indeed in his final years when he surveyed his debates with Bohr, he actually made the statement

The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems.

So the only way to make sense of quantum mechanics according to Einstein is to endorse a statistical interpretation.

Anyway lasers are extremely useful devices but of course in the wrong hands can be used as terrifying weapons. Also idiots shine laser pens in pilots eyes, these people should be forced to face the consequences of their actions. In the right hands of course lasers are a benefit to mankind and a testimony to the ingenuity of scientists all over the world. Here is my tribute to them.




                                     Lasers

 

 Purest light that shines so bright,

 All because a photon takes flight.

Channelled by some clever means,

 Into a set of very intense beams.

 

Once the stuff of science fiction,

 It’s now part of our jurisdiction.

The wise will put you to good use,

But we must guard against abuse

.

James Bond concerned that Goldfinger’s Laser might destroy his manhood. I’ll leave you to decide whether or not that would have been a good thing  😀

Super Conductivity

 One of the most amazing applications of the formalism of quantum mechanics was the explanation by Baarden, Cooper and Schrieffer (BCS) of the phenomenon of Superconductivity. At low temperatures roughly about 4K it was noticed by Onnes that some metals appeared to have a dramatic reduction in their resistance. Whilst classical models were developed describing this phenomenon it wasn't until the 1950's that a microscopic version of the theory was developed. At first sight given the Pauli exclusion principle the phenomenon would seem impossible as it implies many electrons are occupying the same state. Which electrons being Fermions was impossible. Cooper realised at low temperatures there was the possiblity of an interaction between the lattice of the solid and the electrons causing them to effectively pair off. At low temperatures this interaction would be stable as the lattice vibrations would be relatively low. If electrons pair off their total spin becomes zero and they now behave like bosons for which it is possible for many bosons to occupy the same state. Thus the resistance of the metal is lowered BCS quickly realised that the properties of superconductors could be explained and they were awarded the Nobel prize for this work in 1972. 

Compared to the endless debates about the meaning or not of quantum mechanics which are going nowhere. This gives us a real insight into how nature works and ia a triumph of Mankinds ability to understand nature, something that will never come from discussing the meaning of the wave-function. As an interesting foot-note it was discovered in 1986 that some cuprates exhibited Superconductivity at much Higher temperatures than the 'normal ones' As yet there is no convincing explanation for this phenomenon so if you want a Nobel prize get cracking 😅

Here is my poem 

Super Conductivity

 

When it becomes very cold,

Nature becomes extremely bold.

All resistance suddenly dies,

An electric current really flies.

 

Electrons interact with the grid,

Combined in pairs they are hid.

This really ingenious tactic,

Was explained by a quantum mechanic¹⁾

1)    Someone who uses their knowledge of quantum mechanics to explain a feature of nature. In this case it was Cooper (what a clever fellow 😅😅 ).